Logic Anatomy Slides Medical Records: Logic Dept
Logic Anatomy
Distinguishing Form from Content
The Logic Paradox
Case A: The "Crazy" Truth
"All humans are 10 feet tall.
Verdict:
LOGICALLY VALID
The structure is perfect, even if the facts are wrong.
Case B: The "Sensible" Error
"If it rains, the grass gets wet.
Verdict:
LOGICALLY INVALID
The conclusion is likely true, but the reasoning is flawed.
Diagnostic Tools
Informal Fallacy
Errors in content . The evidence is bad, irrelevant, or biased (e.g., Ad Hominem, Straw Man).
Formal Fallacy
Errors in structure . The "shape" of the argument is broken. Even if the facts are 100% true, the conclusion doesn't follow.
"Validity is about the plumbing, not the water."
Plumbing
The Logical Structure (Form)
Water
The Information (Content)
Today, we are inspecting the pipes.
Faulty Forms Worksheet The Logic Lab: Triage
Diagnosis: Formal vs. Informal Fallacies
PHYSICIAN:
DATE:
Lab Report: A "Formal Fallacy" is a flaw in the structure of an argument. An "Informal Fallacy" is a flaw in the content or context. Below are several "patients" (arguments). Determine if their ailment is structural (Formal) or informational (Informal).
Case Patient #102
FORMAL
INFORMAL
"You shouldn't listen to Professor Miller's views on environmental policy. He cheated on his taxes three years ago, so he's a liar."
DIAGNOSIS NOTES (Why?):
Case Patient #103
FORMAL
INFORMAL
"If a person is a professional basketball player, then they are tall. Kevin is tall. Therefore, Kevin is a professional basketball player."
DIAGNOSIS NOTES (Why?):
Case Patient #104
FORMAL
INFORMAL
"All dogs are mammals. My cat is a mammal. Therefore, my cat is a dog."
DIAGNOSIS NOTES (Why?):
Examining the Structure
The best way to spot a Formal Fallacy is to replace the words with symbols (P and Q). If the formula doesn't work with letters, it won't work with words.
Practice: Structural Reduction
Convert the following argument into symbols (If P, then Q. Q. Therefore P.)
"If it is a Friday, the cafeteria serves pizza. It is a Friday. Therefore, it is pizza day."
P =
Q =
Is this structure valid or invalid? Why?
Logic Doctor's Tip
"To find a formal fallacy, try to think of a counter-example. Can you imagine a world where the premises are true but the conclusion is false? If yes, the structure is broken."
Logic Lab Teacher Guide Logic Lab Manual
Teacher Facilitation Guide
TEACHER RESOURCE
Sequence Objective
To move students beyond identifying "bad vibes" in arguments to pinpointing structural invalidity . By the end of this sequence, students should be able to translate verbal arguments into symbolic logic and identify the specific formal fallacy occurring.
Essential Vocabulary
• Formal Fallacy
• Validity vs. Soundness
• Antecedent (P)
• Consequent (Q)
• Distributed Term
• Principle of Charity
Lesson Walkthroughs
Lesson 1: Anatomy of Logic
THE HOOK:
Present Case A & B from the slides. Students will instinctively want to say the "correct facts" argument is more logical. Challenge this immediately: Logic is the math of language; the numbers (facts) can be wrong, but the addition (structure) must be correct.
KEY MISCONCEPTION:
Students often confuse Formal and Informal fallacies. Remind them: Informal = Lies/Distractions. Formal = Bad Math/Broken Shape.
Lessons 2 & 3: Conditional Errors
THE EULER DIAGRAM STRATEGY:
When teaching Affirming the Consequent , use the "Circle of Gills vs. Circle of Sharks." Every shark has gills, but not every gill-bearer is a shark. Students often struggle with the direction of the arrow. Emphasize that P → Q is a one-way street .
Lesson 4: The Undistributed Middle
This is the most "political" fallacy. Use the Senator vs. Terrorist example carefully. It highlights how politicians use shared goals to imply shared identities. Focus on the word "ALL" versus "SOME."
Lesson 5: Logical Renovation
This is the "Principle of Charity" phase. Instead of just "debunking," students act as editors. The goal is not to prove people wrong, but to find out what they would HAVE to believe for their argument to make sense. This builds high-level empathy and critical thinking.
Differentiation & Support
Scaffolding (Struggling Learners)
Use physical manipulatives (hula hoops) for Euler diagrams.
Provide a "Formula Cheat Sheet" for P and Q.
Focus on visual counter-examples over complex text.
Extension (Advanced Learners)
Introduce Truth Tables for validity testing.
Analyze 18th-century philosophy texts for hidden fallacies.
Consequent Diagnosis Slides Affirming the Consequent
The Backward Logic Trap
If P, then Q
Q
∴ P
The "Rain & Umbrella" Error
Premise 1 (The Rule):
"If it is raining, then I carry an umbrella."
P → Q
Premise 2 (The Observation):
"I am carrying an umbrella."
Q (Affirming the Consequent)
The Fallacious Conclusion:
"Therefore, it must be raining."
∴ P
Why is this broken?
The umbrella might be for sun protection , or because I forgot to take it out of my bag, or because I'm being careful .
One effect, many causes!
The Logic Map
THINGS THAT HAPPEN WHEN IT RAINS (Q)
RAINING (P)
You are here!
"P is inside Q, but Q is much bigger than P."
Just because you are inside the big circle (carrying an umbrella) doesn't mean you are inside the small circle (rain).
Case Study: Medical Diagnosis
The Symptom Logic:
"If a patient has Strep Throat (P), they will have a Sore Throat (Q).
This patient has a Sore Throat (Q).
Therefore, they have Strep Throat (P)."
Diagnosis: CRITICAL ERROR
This is Affirming the Consequent. What else could cause a sore throat?
Common Cold
Allergies
Shouting at a concert
Dry air
Rainy Day Logic Worksheet Rainy Day Reasoning
Worksheet // Affirming the Consequent
Case ID: AC-202
LOGICIAN NAME:
DATE:
Identifying the Structure
1. "If you win the lottery, you will be rich. You are rich. Therefore, you won the lottery."
Breakdown:
P = _________________________________
Q = _________________________________
Why it fails:
Provide one alternative reason for Q:
2. "If the power is out, the toaster won't work. The toaster isn't working. The power must be out."
Breakdown:
P = _________________________________
Q = _________________________________
Why it fails:
Provide one alternative reason for Q:
The Logic Map Challenge
Draw an Euler diagram (the circles) for the following rule: "If a creature is a shark, it has gills." Then, show where a goldfish would sit in your diagram.
[ DRAW CIRCLES HERE ]
Instructions:
• Draw a large circle for "Things with Gills" (Q)
• Draw a smaller circle inside it for "Sharks" (P)
• Place an 'X' where "Goldfish" belong.
Critical Analysis:
Does having gills prove you are a shark? Explain based on your map.
Superstition Sleuth
Many superstitions are actually "Affirming the Consequent" errors. Write down one superstition and break it down into P & Q.
Rule (If P then Q):
The Error (Q → P):
Antecedent Analysis Slides Denying the Antecedent
The Inverse Error
If P, then Q
Not P
∴ Not Q
The "No P, No Q" Myth
"If you work hard, you will succeed."
Wait... what if I don't work hard?
"Then I won't succeed!"
This feels true, but is it logically guaranteed ? Can someone succeed through luck, inheritance, or natural talent without "working hard"?
The Logical Gap
The rule only tells us what happens IF P happens. It says absolutely nothing about what happens if P doesn't happen.
~P ⊾ ~Q
(Not P does not prove Not Q)
Diagnostic Comparison
Valid: Modus Tollens
1. If P, then Q
2. Not Q
∴ Not P
"If it's a dog, it's a mammal. It's not a mammal, so it's not a dog."
Invalid: Denying Antecedent
1. If P, then Q
2. Not P
∴ Not Q
"If it's a dog, it's a mammal. It's not a dog, so it's not a mammal."
Case Study: Slogans
"If you drink Glug-Soda, you'll be cool."
Implicit Threat:
Don't drink Glug-Soda? You're uncool.
Advertisers rely on you making the Formal Fallacy . They don't say the second part, they just let your brain fill it in.
The Student Challenge
Can you think of a slogan where "If P then Q" implies that without the product (P), you lose the benefit (Q)?
Museum Field Log Worksheet Museum of Broken Arguments
Field Log // Evidence Collector
LOG NUMBER FALLACY-INV-003
INVESTIGATOR:
STATION:
Field Instructions
You are touring the Logic Error Exhibit . Your task is to examine the "artifacts" (advertisements, slogans, and political clips) provided by your teacher. For each artifact, identify which Formal Fallacy is being used and provide a counter-example.
Exhibit #1
Artifact Type: Print Advertisement
SYMBOLS (P & Q):
P:
Q:
STRUCTURAL ERROR:
Affirming Consequent
Denying Antecedent
THE COUNTER-EXAMPLE:
Exhibit #2
Artifact Type: Social Media Slogan
SYMBOLS (P & Q):
P:
Q:
STRUCTURAL ERROR:
Affirming Consequent
Denying Antecedent
THE COUNTER-EXAMPLE:
Exhibit #3
Artifact Type: Political Soundbite
SYMBOLS (P & Q):
P:
Q:
STRUCTURAL ERROR:
Affirming Consequent
Denying Antecedent
THE COUNTER-EXAMPLE:
Final Diagnostic Assessment
Why does "Denying the Antecedent" often sound like a fair promise in a political speech? (e.g., "If you vote for me, taxes will go down!")
Middle Ground Slides The Undistributed Middle
Broken Connections in Syllogisms
All P are M
The Mustache Fallacy
Premise 1:
"All dictators have mustaches."
Premise 2:
"Mr. Higgins has a mustache."
Fallacious Conclusion:
"Therefore, Mr. Higgins is a dictator."
What went wrong?
The "Middle Term" (Mustache) wasn't distributed properly. Having a mustache is not exclusive to dictators.
"The bridge doesn't reach both shores!"
Undistributed vs. Distributed
MUSTACHE (M)
DICTATOR (P)
HIGGINS (S)
Undistributed Middle
P and S are both in M, but they don't have to touch each other!
HIGGINS (S)
M IS INSIDE P
Distributed Connection
If all M are P, and S is M, then S must be P.
Case Study: Guilt by Association
"Terrorists want to change the government.
The Logic Trap:
The middle term ("Wants change") is not distributed. Millions of people want change for millions of reasons. It doesn't connect the Senator to the Terrorists.
Rhetorical Risk Worksheet Rhetorical Risk Assessment
Diagnosis: Undistributed Middle Terms
LAB SCAN
ANALYST:
CASE DATE:
The Middle Term Rule
In a valid syllogism, the middle term (the word that appears in both premises but not the conclusion) must cover the entire class at least once. If it only covers part of the group, it can't connect the other two terms.
1
The "Creative" Politician
"Successful leaders take risks. My opponent takes risks. Therefore, my opponent is a successful leader."
MIDDLE TERM (M):
WHY IT'S UNDISTRIBUTED:
Draw the Euler Diagram (Circles) below to prove the conclusion doesn't follow:
Diagram Area
2
The "Marketing" Logic
"Elite athletes use AeroShoes. You use AeroShoes. Therefore, you are an elite athlete."
MIDDLE TERM (M):
WHY IT'S UNDISTRIBUTED:
REPAIR CHALLENGE: How could you change Premise 1 to make this argument valid? (Note: It doesn't have to be true, just valid!)
The 'Guilt by Association' Reflection
In your own words, explain how an Undistributed Middle term is often used to make two different things seem the same.
Logical Renovation Slides Logical Renovation
The Art of Charitable Reconstruction
"Don't just tear it down. Build it back better."
The Principle of Charity
When you find a fallacious argument, don't assume the person is "stupid." Assume they have a hidden premise that makes it work.
Our Goal: Find the "Missing Beam."
Step 1: Diagnose
"Where is the structural crack?"
Step 2: Add Premise
"What fact would make this valid?"
Step 3: Evaluate Truth
"Is that new fact actually true?"
Renovation in Action
Broken Original:
"If it's raining, I wear boots.
Fallacy: Affirming Consequent
Renovated Valid Version:
"I ONLY wear boots if it's raining.
Verdict: Valid
The argument is now Valid . But is it Sound ?really only wear boots when it rains? (Probably not!)
Your Lab Mission
You are the Chief Logic Editor for a major debating team. They've handed you a speech full of formal fallacies.
1. DIAGNOSE
Label the formal error.
2. RENOVATE
Change a premise to make it valid.
Logic Editor Challenge Worksheet Logic Editor Challenge
Final Capstone: Reconstruction & Repair
FINAL CLEARANCE
CHIEF EDITOR:
ID CODE:
The Briefing:
Critiquing an argument is easy. Reconstructing one is where the real skill lies. For each "broken" argument below, follow the three steps: Diagnose the structural fallacy, Repair the argument by adding/changing a premise to make it valid, and Evaluate if the new version is actually true (sound).
The Political Promises
"If our city builds more parks, the crime rate will drop. We are building three new parks! Therefore, crime is definitely going down."
A. DIAGNOSIS
Affirming Consequent
Denying Antecedent
Undistributed Middle
B. REPAIR (Rewrite to make it VALID)
C. EVALUATE SOUNDNESS
Is your repaired version actually true? Why or why not?
The Social Influencer
"All genuine artists are creative. Sarah is creative. Therefore, Sarah is a genuine artist."
A. DIAGNOSIS
Affirming Consequent
Denying Antecedent
Undistributed Middle
B. REPAIR (Rewrite to make it VALID)
C. EVALUATE SOUNDNESS
Is your repaired version actually true? Why or why not?
"The logic doctor's work is never done."
